Theorem pm2.64

Description: Theorem *2.64 of WhiteheadRussell p. 107. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.64	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( 𝜑 ∨ ¬ 𝜓 ) → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		orel2	⊢ ( ¬ 𝜓 → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
2	1	jao1i	⊢ ( ( 𝜑 ∨ ¬ 𝜓 ) → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
3	2	com12	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( 𝜑 ∨ ¬ 𝜓 ) → 𝜑 ) )